Why does the Moon always show the same face to us, even though it is constantly orbiting around the Earth? The fact that the Moon rotates on its axis with exactly the same frequency with which it revolves around the Earth might strike many as a surprising coincidence, but in fact, such synchronous motion is not an unusual phenomenon in our solar system. All the other planets in the solar system have been discovered to have most of their moons rotating in the same synchronized way the Moon does with the Earth. Such synchronization between a planet and its moons is mainly due to the "tidal locking process," which I will explain.
|Fig. 1: The rotation of the Earth slows down due to the friction from the tides which is governed by the Moon.|
However, there is one exceptional case of a synchronized motion in our solar system which cannot not be explained by the tidal locking process. When a body is tidally locked to its neighbor, it rotates exactly once as it finishes its orbit around its master. Mercury, on the other hand, exhibits a 3:2 synchronization with the Sun. It rotates on its axis one and a half times during the time it completes one revolution. In this report, I will briefly go over the most important studies that have been made that helped explain this peculiar behavior of Mercury.
Before I start on the motion of Mercury, I will first explain how the tidal locking works, using a nice example of the Earth which is in the process of tidal locking onto the Moon at the moment. Figure 1 qualitatively illustrates how the tides on the Earth produces torque against the Earth's rotation. Two bulges of water on each side of the Earth, which is drastically exaggerated in the figure, are always aligned with the line which connects the Moon and the Earth. But since the Earth is rotating much faster (frequency: 1 day) than the rotation of the bulges (frequency: 1 month), a friction is generated between the water and the Earth. This works as a brake that slows down the rotation of the Earth. It is easy to see that this process will continue until the rotation of the Earth becomes much slower and synchronizes with the revolution of the Moon.
|Fig. 2: The Moon gains energy from the biased gravitational pull from the tides on the Earth.|
|Fig. 3: Synchronized one and a half rotation of Mercury as it orbits around the Sun|